Asynchronous free oscillations of linear mechanical systems: A general appraisal and a digression on a column with a follower force. (September 2017) - Lenci, Stefano
Abstract: The concept of asynchronous oscillatory response of mechanical systems in free vibrations is addressed as an introduction to a definition of asynchronous modes of vibration. Connection of the asynchronous modes with the localization and other dynamical phenomena is discussed. Then, conditions for the occurrence of asynchronous modes are investigated in depth. It is seen that a non-conservative system, with an asymmetric stiffness matrix – caused, for instance, by circulatory loads, may have an asynchronous mode. Yet, it is also seen that non-conservativeness is not actually mandatory. Two- to four-degree-of-freedom models of a column with a follower force are addressed, allowing for a mathematical modelling and phenomenological discussion. Highlights: The concept of asynchronous oscillatory response in free vibrations is addressed. Asynchronous modes of vibration are defined in terms of localization phenomena. Conditions for the occurrence of asynchronous modes are investigated. Systems with an asymmetric stiffness matrix may have asynchronous modes. Two- to four-degree-of-freedom models of a column acted upon by a follower force are discussed.